44. A long, straight coaxial cable consists of two thin, tubular conductors, the inner of radius a and the outer radius b. Current I flows out along one conductor and back along the other. What is the self-inductance per unit length of the cable? (μ₀ is the magnetic constant.)
(A)
(B)
(C)
(D)
(E)

45. The figure shows light passing through a spherical raindrop, undergoing two refractions and total internal reflection. What is the correct relation among angleΦ in the figure, the incident angleθ, and the refractive index of the raindrop n? (A)Φ = 4 sin−1 (sin 2θ /n) − θ (B) Φ= 2 sin−1 (sin 2θ /n) − 2θ (C) Φ = 4 sin−1 (sin θ /n) −θ(D) Φ = 4 sin−1 (sinθ /n) − 2θ(E) Φ= 2 sin−1 (sin θ /n) − 2θ

46. Diffraction imposes a fundamental limit on the ability of optical systems to distinguish closely spaced objects. In general, two peaks are barely distinguishable if the central maximum of one coincides with the first minimum of the other. The two sources become just barely resolved when the Rayleigh criterion is met. Accordingly, what is the Rayleigh criterion for single-slit diffraction? Assume a is the slit width andθmin is the minimum angle separation in the figure. (A) (B) (C) (D)(E)

47. In 1900, the German physicist Max Planck formulated an equation that fit the observed radiance curves forblackbody radiation at all wavelengths: R(λ, T) =, where ℎ is Planck’s constant, c is the speed of light, λ is wavelength, k is Boltzmann’s constant, and T is the absolute temperature. If we integrate the equation over all wavelengths to calculate the total power radiated per unit area, the Stefan-Boltzmann law for blackbody radiation can be derived. Assume A is the area of the radiating surface. Note that， where Γ(n) is the gamma function and  ζ(n) is the Riemann zeta function.For references,. What is the Stefan-Boltzmann law for blackbody radiation?(A) (B)(C) (D) (E)

48. A bullet of mass m is fired horizontally with a speed v into a stationary wooden block of mass M and becomes embedded in it. If the block is suspended by a string of length L (forming a simple pendulum system), what fraction of the initial kinetic energy is lost as mechanical energy during the moment of impact? (A) m / (m + M) (B) M / (m + M) (C) m / M (D) (M - m) / (M + m)

49. Consider a soap bubble and a liquid drop of the same radius. If both have the same surface tension γ, radius R, and external pressure P0, what is the relationship between the internal pressure of the soap bubble (Pbubble) and the internal pressure of the liquid drop (Pdrop)? (A) Pbubble ＞ Pdrop (B) Pbubble ＜ Pdrop (C) Pbubble = Pdrop (D) Cannot be compared

50. An electric diple consists of point charges ±q a distance 2a apart. The potential at an arbitrary point P can be expressed as V(P) = = , where k is the Coulomb constant, r+ is the distance to the point charge +, r− is the distance to the point charge −q. If r is the distance to the dipole center, for r ≫ a, the quantities r+, r−, and r are nearly the same as r2 ≈ r+r−. The difference between the distances from the two charges to P, that is, r− − r+, is approximately equal to 2a cos θ, where θ is the angle as shown in the figure. Eventually, the dipole potential for r ≫ a becomes V(r, θ) = . What is the electric field at an arbitrary position P for r ≫ a? Note that and are unit vectors. (A) (B)(C) (D)(E)

13. 如右圖所示，開關 S 開斷或閉合，電路功率因數均為 0.6，則 XL 與 XC 值各為多少？[台中捷運 110] (A)6Ω，3Ω (B)8Ω，4Ω (C)6Ω，4Ω (D)8Ω，6Ω

14. RC 串聯電路，R = 12Ω，XC = 9Ω，試求電路功率因數為 [台中捷運 110] (A)0.6 電流領前電壓　(B)0.6 電流落後電壓 (C)0.8 電流領前電壓　(D)0.8 電流落後電壓

15. 有一單相交流電路，其電源電壓為 v(t) =，量測到電 路中電流為 i(t) =，則該電路的功率因數 (P.F.) 為何？ [台糖110] (A)0.5 (B)0.707 (C)0.866 (D)1

複選題16. 如右圖所示電路計算交流功率，則下 列何者正確？ [台糖 110] (A) 總平均功率為 1000W (B) 總虛功率為 3000VAR (C) 總視在功率 2000VA (D) 總功率因數 0.707

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